
 Find a augmented matrix 4x5, that has this reduced row-echelon form :

       1/1    0/1    0/1    0/1    1/1
  A =  0/1    1/1    0/1    0/1    2/1
       0/1    0/1    1/1    0/1    3/1
       0/1    0/1    0/1    1/1    4/1

 Create a 4x4 matrix :

       2/1    2/1    3/1    7/1
  B = -5/1   -2/1   -2/1    5/1
       3/1    1/1    7/1    3/1
      -3/1   -1/1   -7/1    2/1

 Multiply A * B : 

       2/1    2/1    3/1    7/1   43/1
      -5/1   -2/1   -2/1    5/1    5/1
       3/1    1/1    7/1    3/1   38/1
      -3/1   -1/1   -7/1    2/1  -18/1


  Verify with the Gauss Jordan function :

       1/1    0/1    0/1    0/1    1/1
       0/1    1/1    0/1    0/1    2/1
       0/1    0/1    1/1    0/1    3/1
       0/1    0/1    0/1    1/1    4/1
